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    "# format the book\n",
    "%matplotlib inline\n",
    "import sys\n",
    "from __future__ import division, print_function\n",
    "import sys\n",
    "sys.path.insert(0,'../code')\n",
    "import book_format\n",
    "book_format.load_style('../code')"
   ]
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   "source": [
    "# Prediction\n",
    "\n",
    "## The Boston Bruins problem\n",
    "\n",
    "In the 2010-11 National Hockey League (NHL) Finals, my beloved Boston\n",
    "Bruins played a best-of-seven championship series against the despised\n",
    "Vancouver Canucks. Boston lost the first two games 0-1 and 2-3, then won\n",
    "the next two games 8-1 and 4-0. At this point in the series, what is the\n",
    "probability that Boston will win the next game, and what is their\n",
    "probability of winning the championship?\n",
    "\n",
    "As always, to answer a question like this, we need to make some\n",
    "assumptions. First, it is reasonable to believe that goal scoring in\n",
    "hockey is at least approximately a Poisson process, which means that it\n",
    "is equally likely for a goal to be scored at any time during a game.\n",
    "Second, we can assume that against a particular opponent, each team has\n",
    "some long-term average goals per game, denoted $\\lambda$.\n",
    "\n",
    "Given these assumptions, my strategy for answering this question is\n",
    "\n",
    "1.  Use statistics from previous games to choose a prior distribution\n",
    "    for $\\lambda$.\n",
    "\n",
    "2.  Use the score from the first four games to estimate $\\lambda$ for\n",
    "    each team.\n",
    "\n",
    "3.  Use the posterior distributions of $\\lambda$ to compute distribution\n",
    "    of goals for each team, the distribution of the goal differential,\n",
    "    and the probability that each team wins the next game.\n",
    "\n",
    "4.  Compute the probability that each team wins the series.\n",
    "\n",
    "To choose a prior distribution, I got some statistics from\n",
    "<http://www.nhl.com>, specifically the average goals per game for each\n",
    "team in the 2010-11 season. The distribution is roughly Gaussian with\n",
    "mean 2.8 and standard deviation 0.3.\n",
    "\n",
    "The Gaussian distribution is continuous, but we’ll approximate it with a\n",
    "discrete Pmf. `thinkbayes` provides `MakeGaussianPmf` to do exactly\n",
    "that:\n",
    "\n",
    "```python\n",
    "def MakeGaussianPmf(mu, sigma, num_sigmas, n=101):\n",
    "    pmf = Pmf()\n",
    "    low = mu - num_sigmas*sigma\n",
    "    high = mu + num_sigmas*sigma\n",
    "\n",
    "    for x in numpy.linspace(low, high, n):\n",
    "        p = scipy.stats.norm.pdf(mu, sigma, x)\n",
    "        pmf.Set(x, p)\n",
    "    pmf.Normalize()\n",
    "    return pmf\n",
    "```\n",
    "\n",
    "`mu` and `sigma` are the mean and standard\n",
    "deviation of the Gaussian distribution. `num_sigmas` is the number of\n",
    "standard deviations above and below the mean that the Pmf will span, and\n",
    "`n` is the number of values in the Pmf.\n",
    "\n",
    "Again we use `numpy.linspace` to make an array of\n",
    "`n` equally spaced values between `low` and\n",
    "`high`, including both.\n",
    "\n",
    "`norm.pdf` evaluates the Gaussian probability density function (PDF).\n",
    "\n",
    "Getting back to the hockey problem, here’s the definition for a suite of\n",
    "hypotheses about the value of $\\lambda$.\n",
    "\n",
    "```python\n",
    "class Hockey(thinkbayes.Suite):\n",
    "\n",
    "    def __init__(self):\n",
    "        pmf = thinkbayes.MakeGaussianPmf(mu=2.7, sigma=0.3, num_sigmas=4)\n",
    "        thinkbayes.Suite.__init__(self, pmf)\n",
    "```\n",
    "\n",
    "So the prior distribution is Gaussian with mean 2.7, standard deviation\n",
    "0.3, and it spans 4 sigmas above and below the mean.\n",
    "\n",
    "As always, we have to decide how to represent each hypothesis; in this\n",
    "case I represent the hypothesis that $\\lambda=x$ with the floating-point\n",
    "value `x`."
   ]
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   "source": [
    "## Poisson processes\n",
    "\n",
    "In mathematical statistics, a **process** is a stochastic\n",
    "model of a physical system (“stochastic” means that the model has some\n",
    "kind of randomness in it). For example, a Bernoulli process is a model\n",
    "of a sequence of events, called trials, in which each trial has two\n",
    "possible outcomes, like success and failure. So a Bernoulli process is a\n",
    "natural model for a series of coin flips, or a series of shots on goal.\n",
    "\n",
    "A Poisson process is the continuous version of a Bernoulli process,\n",
    "where an event can occur at any point in time with equal probability.\n",
    "Poisson processes can be used to model customers arriving in a store,\n",
    "buses arriving at a bus stop, or goals scored in a hockey game.\n",
    "\n",
    "In many real systems the probability of an event changes over time.\n",
    "Customers are more likely to go to a store at certain times of day,\n",
    "buses are supposed to arrive at fixed intervals, and goals are more or\n",
    "less likely at different times during a game.\n",
    "\n",
    "But all models are based on simplifications, and in this case modeling a\n",
    "hockey game with a Poisson process is a reasonable choice. Heuer, Müller\n",
    "and Rubner (2010) analyze scoring in a German soccer league and come to\n",
    "the same conclusion; see\n",
    "<http://www.cimat.mx/Eventos/vpec10/img/poisson.pdf>.\n",
    "\n",
    "The benefit of using this model is that we can compute the distribution\n",
    "of goals per game efficiently, as well as the distribution of time\n",
    "between goals. Specifically, if the average number of goals in a game is\n",
    "`lam`, the distribution of goals per game is given by the\n",
    "Poisson PMF:"
   ]
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    "def EvalPoissonPmf(k, lam):\n",
    "    return (lam)**k * math.exp(-lam) / math.factorial(k)"
   ]
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   "source": [
    "And the distribution of time between goals is given by the exponential\n",
    "PDF:"
   ]
  },
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   "source": [
    "def EvalExponentialPdf(x, lam):\n",
    "    return lam * math.exp(-lam * x)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I use the variable `lam` because `lambda` is a\n",
    "reserved keyword in Python. Both of these functions are in\n",
    "`thinkbayes.py`."
   ]
  },
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   "source": [
    "## The posteriors\n",
    "\n",
    "![Posterior distribution of the number of goals per\n",
    "game.](figs/hockey1.pdf)\n",
    "\n",
    "[fig.hockey1]\n",
    "\n",
    "Now we can compute the likelihood that a team with a hypothetical value\n",
    "of `lam` scores `k` goals in a game:\n",
    "\n",
    "```python\n",
    "# class Hockey\n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam = hypo\n",
    "        k = data\n",
    "        like = thinkbayes.EvalPoissonPmf(k, lam)\n",
    "        return like\n",
    "```\n",
    "\n",
    "Each hypothesis is a possible value of $\\lambda$; `data` is\n",
    "the observed number of goals, `k`.\n",
    "\n",
    "With the likelihood function in place, we can make a suite for each team\n",
    "and update them with the scores from the first four games."
   ]
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VBuBVpRrfXinAzzdKwbTUkv+5HGiyc8LcYV4wEz58GUe5QoWPPj2FyhoerKwsAQAL/j4c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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1adee907828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from hockey import *\n",
    "import thinkplot\n",
    "\n",
    "suite1 = Hockey('bruins')\n",
    "suite1.UpdateSet([0, 2, 8, 4])\n",
    "\n",
    "suite2 = Hockey('canucks')\n",
    "suite2.UpdateSet([1, 3, 1, 0])\n",
    "\n",
    "thinkplot.PrePlot(num=2)\n",
    "thinkplot.Pmf(suite1)\n",
    "thinkplot.Pmf(suite2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 7.1: Posterior distribution of the number of goals per\n",
    "game.\n",
    "\n",
    "Figure 7.1 shows the resulting posterior distributions for\n",
    "`lam`. Based on the first four games, the most likely values\n",
    "for `lam` are 2.6 for the Canucks and 2.9 for the Bruins."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The distribution of goals\n",
    "\n",
    "To compute the probability that each team wins the next game, we need to\n",
    "compute the distribution of goals for each team.\n",
    "\n",
    "If we knew the value of `lam` exactly, we could use the\n",
    "Poisson distribution again. `thinkbayes` provides a method that computes\n",
    "a truncated approximation of a Poisson distribution:\n",
    "\n",
    "```python\n",
    "def MakePoissonPmf(lam, high):\n",
    "    pmf = Pmf()\n",
    "    for k in xrange(0, high+1):\n",
    "        p = EvalPoissonPmf(k, lam)\n",
    "        pmf.Set(k, p)\n",
    "    pmf.Normalize()\n",
    "    return pmf\n",
    "```\n",
    "\n",
    "The range of values in the computed Pmf is from 0 to `high`.\n",
    "So if the value of `lam` were exactly 3.4, we would compute:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lam = 3.4\n",
    "goal_dist = thinkbayes.MakePoissonPmf(lam, 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I chose the upper bound, 10, because the probability of scoring more\n",
    "than 10 goals in a game is quite low.\n",
    "\n",
    "That’s simple enough so far; the problem is that we don’t know the value\n",
    "of `lam` exactly. Instead, we have a distribution of possible\n",
    "values for `lam`.\n",
    "\n",
    "For each value of `lam`, the distribution of goals is\n",
    "Poisson. So the overall distribution of goals is a mixture of these\n",
    "Poisson distributions, weighted according to the probabilities in the\n",
    "distribution of `lam`.\n",
    "\n",
    "Given the posterior distribution of `lam`, here’s the code\n",
    "that makes the distribution of goals:\n",
    "\n",
    "```python\n",
    "def MakeGoalPmf(suite):\n",
    "    metapmf = thinkbayes.Pmf()\n",
    "\n",
    "    for lam, prob in suite.Items():\n",
    "        pmf = thinkbayes.MakePoissonPmf(lam, 10)\n",
    "        metapmf.Set(pmf, prob)\n",
    "\n",
    "    mix = thinkbayes.MakeMixture(metapmf)\n",
    "    return mix\n",
    "```\n",
    "\n",
    "For each value of `lam` we make a Poisson Pmf and add it to\n",
    "the meta-Pmf. I call it a meta-Pmf because it is a Pmf that contains\n",
    "Pmfs as its values.\n",
    "\n",
    "Then we use `MakeMixture` to compute the mixture (we saw\n",
    "`MakeMixture` in Section [mixture])."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mo9Xp8FFCLjR/LVgjt8SayGDc18cTkg6a9gIAyaeLsfzN/ahv0M9FtrWRYdn8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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1adef11b1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "goal_dist1 = MakeGoalPmf(suite1)\n",
    "goal_dist2 = MakeGoalPmf(suite2)\n",
    "\n",
    "thinkplot.Clf()\n",
    "thinkplot.PrePlot(num=2)\n",
    "thinkplot.Pmf(goal_dist1)\n",
    "thinkplot.Pmf(goal_dist2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 7.2: Distribution of goals in a single game.\n",
    "\n",
    "Figure 7.2 shows the resulting distribution of goals for the\n",
    "Bruins and Canucks. The Bruins are less likely to score 3 goals or fewer\n",
    "in the next game, and more likely to score 4 or more."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The probability of winning\n",
    "\n",
    "To get the probability of winning, first we compute the distribution of\n",
    "the goal differential:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "goal_dist1 = MakeGoalPmf(suite1)\n",
    "goal_dist2 = MakeGoalPmf(suite2)\n",
    "diff = goal_dist1 - goal_dist2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The subtraction operator invokes `Pmf.__sub__`, which enumerates pairs\n",
    "of values and computes the difference. Subtracting two distributions is\n",
    "almost the same as adding, which we saw in Section [addends].\n",
    "\n",
    "If the goal differential is positive, the Bruins win; if negative, the\n",
    "Canucks win; if 0, it’s a tie:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.457996492072\n",
      "0.370293408955\n",
      "0.171710098973\n"
     ]
    }
   ],
   "source": [
    "p_win = diff.ProbGreater(0)\n",
    "p_loss = diff.ProbLess(0)\n",
    "p_tie = diff.Prob(0)\n",
    "print(p_win)\n",
    "print(p_loss)\n",
    "print(p_tie)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the distributions from the previous section, `p_win` is 46%,\n",
    "`p_loss` is 37%, and `p_tie` is 17%.\n",
    "\n",
    "In the event of a tie at the end of “regulation play,” the teams play\n",
    "overtime periods until one team scores. Since the game ends immediately\n",
    "when the first goal is scored, this overtime format is known as “sudden\n",
    "death.”"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sudden death\n",
    "\n",
    "To compute the probability of winning in a sudden death overtime, the\n",
    "important statistic is not goals per game, but time until the first\n",
    "goal. The assumption that goal-scoring is a Poisson process implies that\n",
    "the time between goals is exponentially distributed.\n",
    "\n",
    "Given `lam`, we can compute the time between goals like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "lam = 3.4\n",
    "time_dist = thinkbayes.MakeExponentialPmf(lam, high=2, n=101)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`high` is the upper bound of the distribution. In this case I\n",
    "chose 2, because the probability of going more than two games without\n",
    "scoring is small. `n` is the number of values in the Pmf.\n",
    "\n",
    "If we know `lam` exactly, that’s all there is to it. But we\n",
    "don’t; instead we have a posterior distribution of possible values. So\n",
    "as we did with the distribution of goals, we make a meta-Pmf and compute\n",
    "a mixture of Pmfs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def MakeGoalTimePmf(suite):\n",
    "    metapmf = thinkbayes.Pmf()\n",
    "\n",
    "    for lam, prob in suite.Items():\n",
    "        pmf = thinkbayes.MakeExponentialPmf(lam, high=2, n=2001)\n",
    "        metapmf.Set(pmf, prob)\n",
    "\n",
    "    mix = thinkbayes.MakeMixture(metapmf, name=suite.name)\n",
    "    return mix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 7.3 below shows the resulting distributions. For time values\n",
    "less than one period (one third of a game), the Bruins are more likely\n",
    "to score. The time until the Canucks score is more likely to be longer.\n",
    "\n",
    "I set the number of values, `n`, fairly high in order to\n",
    "minimize the number of ties, since it is not possible for both teams to\n",
    "score simultaneously.\n",
    "\n",
    "Now we compute the probability that the Bruins score first:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "time_dist1 = MakeGoalTimePmf(suite1)\n",
    "time_dist2 = MakeGoalTimePmf(suite2)\n",
    "p_overtime = thinkbayes.PmfProbLess(time_dist1, time_dist2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the Bruins, the probability of winning in overtime is 52%.\n",
    "\n",
    "Finally, the total probability of winning is the chance of winning at\n",
    "the end of regulation play plus the probability of winning in overtime."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p_tie = diff.Prob(0)\n",
    "p_overtime = thinkbayes.PmfProbLess(time_dist1, time_dist2)\n",
    "\n",
    "p_win = diff.ProbGreater(0) + p_tie * p_overtime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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eP5vPnK3Hyk3k8PN1ZdSIm23HX68/wuatFfcIEBERERG5llT8Xwfh3mZGRzW2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\nxP8HnbvVK1gEmJIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1adef5cf710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "thinkplot.PrePlot(num=2)\n",
    "thinkplot.Pmf(time_dist1)\n",
    "thinkplot.Pmf(time_dist2)\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Figure 7.3: Distribution of time between goals.\n",
    "\n",
    "For the Bruins, the overall chance of winning the next game is 55%.\n",
    "\n",
    "To win the series, the Bruins can either win the next two games or split\n",
    "the next two and win the third. Again, we can compute the total\n",
    "probability:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.57142746956373758"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# win the next two\n",
    "p_series = p_win**2\n",
    "\n",
    "# split the next two, win the third\n",
    "p_series += 2 * p_win * (1-p_win) * p_win\n",
    "p_series"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Bruins chance of winning the series is 57%. And in 2011, they did."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Discussion\n",
    "\n",
    "As always, the analysis in this chapter is based on modeling decisions,\n",
    "and modeling is almost always an iterative process. In general, you want\n",
    "to start with something simple that yields an approximate answer,\n",
    "identify likely sources of error, and look for opportunities for\n",
    "improvement.\n",
    "\n",
    "In this example, I would consider these options:\n",
    "\n",
    "-   I chose a prior based on the average goals per game for each team.\n",
    "    But this statistic is averaged across all opponents. Against a\n",
    "    particular opponent, we might expect more variability. For example,\n",
    "    if the team with the best offense plays the team with the worst\n",
    "    defense, the expected goals per game might be several standard\n",
    "    deviations above the mean.\n",
    "\n",
    "-   For data I used only the first four games of the championship\n",
    "    series. If the same teams played each other during the regular\n",
    "    season, I could use the results from those games as well. One\n",
    "    complication is that the composition of teams changes during the\n",
    "    season due to trades and injuries. So it might be best to give more\n",
    "    weight to recent games.\n",
    "\n",
    "-   To take advantage of all available information, we could use results\n",
    "    from all regular season games to estimate each team’s goal scoring\n",
    "    rate, possibly adjusted by estimating an additional factor for each\n",
    "    pairwise match-up. This approach would be more complicated, but it\n",
    "    is still feasible.\n",
    "\n",
    "For the first option, we could use the results from the regular season\n",
    "to estimate the variability across all pairwise match-ups. Thanks to\n",
    "Dirk Hoag at <http://forechecker.blogspot.com/>, I was able to get the\n",
    "number of goals scored during regulation play (not overtime) for each\n",
    "game in the regular season.\n",
    "\n",
    "Teams in different conferences only play each other one or two times in\n",
    "the regular season, so I focused on pairs that played each other 4–6\n",
    "times. For each pair, I computed the average goals per game, which is an\n",
    "estimate of $\\lambda$, then plotted the distribution of these estimates.\n",
    "\n",
    "The mean of these estimates is 2.8, again, but the standard deviation is\n",
    "0.85, substantially higher than what we got computing one estimate for\n",
    "each team.\n",
    "\n",
    "If we run the analysis again with the higher-variance prior, the\n",
    "probability that the Bruins win the series is 80%, substantially higher\n",
    "than the result with the low-variance prior, 57%.\n",
    "\n",
    "So it turns out that the results are sensitive to the prior, which makes\n",
    "sense considering how little data we have to work with. Based on the\n",
    "difference between the low-variance model and the high-variable model,\n",
    "it seems worthwhile to put some effort into getting the prior right.\n",
    "\n",
    "The code and data for this chapter are available from\n",
    "<http://thinkbayes.com/hockey.py> and\n",
    "<http://thinkbayes.com/hockey_data.csv>. For more information see\n",
    "Section [download]."
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    "## Exercises\n",
    "\n",
    "If buses arrive at a bus stop every 20 minutes, and you arrive at the\n",
    "bus stop at a random time, your wait time until the bus arrives is\n",
    "uniformly distributed from 0 to 20 minutes.\n",
    "\n",
    "But in reality, there is variability in the time between buses. Suppose\n",
    "you are waiting for a bus, and you know the historical distribution of\n",
    "time between buses. Compute your distribution of wait times.\n",
    "\n",
    "Hint: Suppose that the time between buses is either 5 or 10 minutes with\n",
    "equal probability. What is the probability that you arrive during one of\n",
    "the 10 minute intervals?\n",
    "\n",
    "I solve a version of this problem in the next chapter.\n",
    "\n",
    "Suppose that passengers arriving at the bus stop are well-modeled by a\n",
    "Poisson process with parameter $\\lambda$. If you arrive at the stop and\n",
    "find 3 people waiting, what is your posterior distribution for the time\n",
    "since the last bus arrived.\n",
    "\n",
    "I solve a version of this problem in the next chapter.\n",
    "\n",
    "Suppose that you are an ecologist sampling the insect population in a\n",
    "new environment. You deploy 100 traps in a test area and come back the\n",
    "next day to check on them. You find that 37 traps have been triggered,\n",
    "trapping an insect inside. Once a trap triggers, it cannot trap another\n",
    "insect until it has been reset.\n",
    "\n",
    "If you reset the traps and come back in two days, how many traps do you\n",
    "expect to find triggered? Compute a posterior predictive distribution\n",
    "for the number of traps.\n",
    "\n",
    "Suppose you are the manager of an apartment building with 100 light\n",
    "bulbs in common areas. It is your responsibility to replace light bulbs\n",
    "when they break.\n",
    "\n",
    "On January 1, all 100 bulbs are working. When you inspect them on\n",
    "February 1, you find 3 light bulbs out. If you come back on April 1, how\n",
    "many light bulbs do you expect to find broken?\n",
    "\n",
    "In the previous exercise, you could reasonably assume that an event is\n",
    "equally likely at any time. For light bulbs, the likelihood of failure\n",
    "depends on the age of the bulb. Specifically, old bulbs have an\n",
    "increasing failure rate due to evaporation of the filament.\n",
    "\n",
    "This problem is more open-ended than some; you will have to make\n",
    "modeling decisions. You might want to read about the Weibull\n",
    "distribution (<http://en.wikipedia.org/wiki/Weibull_distribution>). Or\n",
    "you might want to look around for information about light bulb survival\n",
    "curves."
   ]
  }
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